WBJEE · Maths · Hyperbola
If the straight line \((a-1) x-b y+4=0\) is normal to the hyperbola \(x y=1\), then which of the following does not hold?
- A \(a>1, b>0\)
- B \(a>1, b < 0\)
- C \(a < 1, b < 0\)
- D \(a < 1, b>0\)
Answer & Solution
Correct Answer
(C) \(a < 1, b < 0\)
Step-by-step Solution
Detailed explanation
Given equation of straight line is \[ (a-1) x-b y+4=0 \] Slope \(=-\frac{\text { Coefficient of } x}{\text { Coefficient of } y}\) \(=\frac{-(a-1)}{-b}=\frac{a-1}{b}\) Equation of hyperbola is \(x y=1\) \(\Rightarrow \quad y=\frac{1}{x}\)…
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